Sochi, where the 2014 Winter Olympic Games opened this week, has been twinned since 1959 with the genteel English town of Cheltenham. The mind boggles at first, but then begins to see the similarities: both spa towns, both fashionable 19th-century resorts, both destinations for monarchs and presidents, both provincial centres of affluence, and so on. Similarities exhausted, the differences come flooding back. Sochi is not only subtropical, coastal and three times the size of Cheltenham, it is also in the Caucasus - a region for which Britain has no real equivalent.

Comparisons could be made with the Lake District - inspiration and epitome of Romanticism, archetype of Nature-with-a-capital-N. In Wordsworth's poems, the humble Lucy represents a venerable simplicity, as do Caucasian maidens Bela, in Mikhail Lermontov's novel A Hero of Our Time (1839), and Dina in Leo Tolstoy's The Prisoner of the Caucasus (1872).

And just as the jaded of London head to the Lakes for spiritual renewal, so Lermontov's Pechorin and Tolstoy's Olenin leave St Petersburg and Moscow respectively for the Caucasus, seeking and finding stupendous natural beauty, and a society without decadence, pretension, or hypocrisy. "On leaving Moscow, [Olenin] was in that happy state of mind in which a young man, conscious of past mistakes, suddenly says to himself, That was not the real thing.'"

But where the Lake District is merely hilly, the Caucasus is Russia's biggest mountain range, and Mount Elbrus is Europe's highest peak - three times higher than Ben Nevis. The range's southern reaches - the Trans­caucasus - covers the countries of Georgia, Armenia and Azerbaijan, while its northern part - the Ciscaucasus - covers such Russian autonomous republics as North Ossetia, Ingushetia, Chechnya and Dagestan.

The isthmus on which the Caucasus is located connects Russia to the Middle East, and separates the Black Sea from the Caspian. Classical scholars know the region as the one where Prometheus had his liver eaten daily by an eagle; where Jason sought the Golden Fleece and found Medea in the Georgian city of Colchis. Byron, though he never visited the region, described the mountains (in "Heaven and Earth") as "So varied and so terrible in beauty" with "perpendicular places, where the foot/ Of man would tremble, could he reach them - yes,/ Ye look eternal!"

Caucasian leader Imam Shamil surrenders to the Russian general Count Baryatinsky in 1859

In this sense, a closer British equivalent would be the Scottish Highlands. And both the Highlands and the Caucasus are associated, in the imperial mind, with wild clans and martial traditions. Both regions resisted domin­ation sufficiently long and hard that their leaders' names are still remembered - William Wallace, Robert the Bruce; Hadji Murat and Imam Shamil (the last two from the hundred years' war of Russia's Caucasian conquest which ended in 1864).

In the literature of the time, these mountain warriors gained not only the admiration but some of the sympathy of those sent to conquer them. The eponymous hero of Walter Scott's Waverley (1814) even defects to the Jacobites when sent to put down their uprising, having fallen under the influence of Bonnie Prince Charlie and one of his sexier female devotees.

Scott's works were hugely popular in Russia, and influenced Tolstoy, whose final novella Hadji Murat (1896-1904) describes the last stand of the eponymous Avar leader with admiration, and the court of Nicholas I with loathing and contempt.

In an earlier Tolstoyan story, the eponymous Cossacks are presented as right to admire their brave Chechen enemies more than the Russian soldiers - often snobbish, lazy, and militarily inept - who are billeted on them in the Caucasus. But, like the Grand Tourists who were busy discovering Switzerland at this time, the Russian officers find their conceptions of God and man altered by the sublimity they encountered in the mountains.

And just as Wordsworth, Coleridge, Byron and Shelley pioneered a Romantic appreciation of the Alps, so Russian poets such as Gavrila Derzhavin and Alexander Pushkin did the same for the Caucasus. In his 1821 poem, "A Prisoner of the Caucasus", Pushkin recounts that "My poetic meditation/Recalled to me the Caucasus", where Mount Bashtau "was for me a new Parnassus./ Will I ever forget its gritty heights,/ Its gushing springs, its withering plains,/ Its burning deserts, regions where you shared with me/The impressions of a young soul?"

By the time Tolstoy's nobleman Olenin arrives in the Caucasus in 1852, he is primed to have a Romantic response. Initially disappointed at seeing the mountains under mist, he awakes the following morning to find them in full sunlight: faced with "the infinitude of all that beauty, he became afraid that it was but a phantasm or a dream" - but then "he began by slow degrees to be penetrated by their beauty and at length to feel the mountains".

Olenin appreciates that life in the Caucasus is better for the body, as well as the soul, than anywhere else in Russia. The climate is good, the food and wine better, and life expectancy (violent death aside) correspondingly high. After a few weeks in a Chechen village on the Terek river, "Olenin looked quite a different man ... Instead of a sallow complexion, the result of nights turned into day, his cheeks, his forehead, and the skin behind his ears were now red with healthy sunburn ... his whole person breathed health, joy, and satisfaction."

Byron was an even greater success in Russia than Scott, and both Lermontov's Pechorin and Pushkin's "Prisoner of the Caucasus" are Byronic heroes - sensitive, cynical, brave, and rash. Native women love them at their own risk; it is not entirely beside the point that From Russia with Love's Tatiana Romanova decides that she loves James Bond on seeing from his file that he looks like Pechorin.

But not all the Russians who brave the Caucasus are also cads. Olenin wants to shed his Petersburg pseudo-civilisation to marry and become a Cossack. His marriage plans fall through, and he leaves the village where he has lived for a year broken-hearted after a tearful parting from his father-figure Eroshka. Then - in a twist resembling the ending of Shirley Valentine - he turns his head, and sees Eroshka discussing village matters with his beloved, as if Olenin had never existed. The life of the Caucasus goes on without him.

Tolstoy's earlier novella reprised the trope of the Russian prisoner held captive in the Caucasus - one that first featured in Pushkin's poem and was followed by several other works of the same theme and title, including a 1858 opera by Cesar Cui. In all of these, the prisoner spends his captivity observing and wondering at Caucasian life, alienated from the sophisticated metropolitan culture to which he belongs but unable to assimilate - a condition that fetters him as much as his chains. He is eventually helped to escape by a nobly savage maid whose adoring femininity is the counterpoint to Caucasian hyper-masculinity. In Pushkin's version the prisoner abandons his girl, who commits suicide in a stream as he strides towards the Cossacks and freedom. In Tolstoy's, by contrast, Zhilin is only ever kindly fraternal to the 13-year-old who liberates him.

Tolstoy is also distinctive by virtue of his criticism of the imperial project. Writers such as Derzhavin, Pushkin and Lermontov may have admired the Caucasus, but they also believed in Russia's right to rule there. Pushkin's "Prisoner of the Caucasus" ends with imperialist aplomb:

So the furious shouts of war were silenced:/ All was subjected by the Russian sword/ The proud sons of the Caucasus/ Fought, suffered terrible losses;/ But spilling our blood did not save you/ Nor did your charmed armour/ Nor the mountains, nor your intrepid horses,/ Nor your love of wild freedom!

In the Soviet period, the mission of bringing literacy to the Caucasus, along with the imperial language and literature, European mores and a degree of equality for women, parallels the British project to "civilise" the Raj. Both succeeded Muslim powers as imperialists, and drew regional boundaries partly with the aim of undermining ethnic loyalties - to divide and rule.

They also held the native peoples in different degrees of respect: particularly respected in both cases were the mountain fighters, who were eventually transformed into the crack troops of the imperial power: the Caucasian regiments were a Russian version of Britain's Gurkhas. They represented a warrior culture that the imperialists were conscious of having lost, if they had ever possessed one.

As Pushkin's prisoner observes: "A Circassian is festooned with weaponry; he takes pride and comfort in it." They are men "born for war". During the recent conflict in Chechnya, Russian consciousness of belonging to a less military culture can be seen as similarly inflected by fear.

Today, how Russians see the Caucasus depends on many variables, including where they live (Novosibirsk is as far away from Sochi as London is). But one of the most interesting is age. Older people remember it as a place of peace, Soviet development, sunny holidays and the production of fruit, wine and flowers; in the Soviet era, many regarded the region's living standards with envy. Films such as Leonid Gaidai's romantic comedy Kidnapping Caucasian Style (1967) up-ends the Pushkin and Tolstoy plots. Russians were shocked, after the 1991 break-up of the USSR, to see how abruptly places such as Georgia became hostile (and foreign) and wars broke out in Chechnya and South Ossetia.

Writers sought to reflect the new mood. In Vladimir Makanin's 1994 The Prisoner of the Caucasus the prisoner is not Russian but a 16-year-old Chechen hostage who sexually arouses his Russian captor. In some respects it reads uncannily like Tolstoy's story of the same title; ostensibly the roles are reversed, as the captive combines the roles of Caucasian warrior with that of Caucasian maid.

Yet it is the Russians, as before, who are captive to the Caucasians they are trying to conquer. A local dealer who barters with a Russian officer comments: "What sort of a prisoner am I? ... It's you who are a prisoner here!" The Soviet slogan "Long live the inviolable friendship of peoples" is quoted sardonically by one Russian, and laughed at by another. Soviet friendship is history. Tsarist conflict is revived - but without the Romantic idealism.

Victor Pelevin's 1995 story "Chechen Hats in the Towers" is a satire in which Chechens capture the Kremlin, and the security services try to hush this up. Voluntary hostages are permitted, and so many fame-hungry Russians stream to the Kremlin that eventually a $5,000 entrance fee is charged. Here there is no idealism on either side.

Russia's athletes in Sochi were born during the Soviet collapse or its aftermath. They have no fond memories of holidays in Dagestani resorts; they grew up watching news footage of Russian teenagers wounded, tortured or dead in Chechnya.

And yet, amid the vestiges of Soviet education, they will also have inherited the Russian exhilaration at the Caucasus from Pushkin, Lermontov and Tolstoy. As Olenin approaches Chechnya, he sees: "Two Cossacks ride by, their guns in their cases swinging rhythmically behind their backs, the white and bay legs of their horses mingling confusedly ... and the mountains! Beyond the Terek rises the smoke from a Tartar village ... and the mountains! The sun has risen and glitters on the Terek, now visible beyond the reeds ... and the mountains! From the village comes a Tartar wagon, and women, beautiful young women, pass by ... and the mountains! Abreks canter about the plain, and here am I driving along and do not fear them! I have a gun, and strength and youth ... and the mountains!"

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